virtual testing of bridges for life cycle reliability...

IABMAS´08SEOUL, SOUTH KOREA

JULY 2008

PUKL et al.:VIRTUAL TESTING OF BRIDGES FOR LIFE CYCLE RELIABILITY ASSESSMENT

1

VIRTUAL TESTING OF BRIDGES FOR LIFE CYCLE RELIABILITY ASSESSMENT

Radomír

Pukl

and Vladimír ČervenkaČervenka

Consulting, Prague, Czech Republic

Drahomír

Novák and Břetislav TeplýBrno University of Technology, Czech Republic

Konrad

Bergmeister

and Alfred StraussUniversity of Natural Resources and Applied Life Sciences, Vienna, Austria

Outline:SARA software system –

Structural Analysis and Reliability Assessment –

modeling of structural behavior

three core components:Nonlinear computer simulation of damage in concrete structures

Probabilistic-based assessment of structural safety and reliabilityProbabilistic modeling of material degradation


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SARA projectStructural Analysis and Reliability Assessment

assessment of structural reliability based on nonlinear finite element analysisinternational research team –

Italy, Austria, Czech Republicleader -

Prof. Konrad Bergmeisteroriginal purpose –

safety of bridges –

Brennero

highway

presentation at: IABMAS, Euro-C, ICASP, ICOSSAR, SHMII, IALCCE, …next projects: Sustainable bridges, VITESPO, …

SARA system -

integration

of nonlinear FEM and advanced probabilistic methods (LHS)open architecture:

degradation analysis –

life-cycle reliabilityspatial variability of structural (material) properties

dynamic damage identification


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SARA main

components:


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Nonlinear finite element analysis of reinforced concrete structures -

software

ATENA

Numerical

core

is

based

on realistic

material

model for concrete

Text

Computer simulation of damage

in engineering

structures

–

VIRTUAL TESTING


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Model for concrete:

damage mechanics

objectivity (FE mesh independent)deterministic size-effect

Concrete

in tension

smeared crack approach

nonlinear fracture mechanicstensile softening after crackingcrack band method


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Solid

finite

elements

in ATENA

nodal points with 3 displacement DOFs

layered integration points

• brick

• tetrahedron

• wedge

• linear

• quadratic

• layered

shell/plate elements

• higher

order


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Steel reinforcement in concrete

in ATENA

• discrete reinforcing bars

• smeared reinforcement

• perfect

bond

• bond-slip law

• prestressing

cables


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Program ATENA

Well-balanced approach

for practical applications

of advanced FEM in civil engineering

Numerical core

-

state-of-art background + Graphical user environment-

visualization + interaction

-2.431E+00

-2.200E+00

-2.000E+00

-1.800E+00

-1.600E+00

-1.400E+00

-1.200E+00

-1.000E+00

-8.000E-01

-6.000E-01

-4.000E-01

-2.000E-01

0 000E+00 M2:

Rea

ctio

ns C

ompo

nent

2


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Fields of application:

structural detailsanchorsframe corners

precast elements

transport infrastructuretunnelsbridges

buildings (high rise)hallscontainments (nuclear power plants)

examples

from Prague, Czech Republic


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Analysis of structural details

fasteners in concrete –

pull out test Step 32, RILEM axi A2, d=150, a=2d, K=oo Scalar: rendering, Basic material, in nodes, Tensile Strength, Sig T(2), <3.000E-03;3.000E+00>[MPa]

3.000E-033.300E-016.600E-019.900E-011.320E+00

1.680E+002.010E+002.340E+002.670E+003.000E+00


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Charles bridge

in Prague, Czech Republic, founded

1357 -

650 years

old


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c


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S tep 26, NSf-UZL - nevyztuzene osteni 300, MSU, zima, liniove pruzne ulozeni Scalars:iso-areas, Basic material, in nodes, Principal Stress, Max., <-5.027E-01;9.964E-01>[MP a]

-5.027E-01-4.500E-01-3.000E-01-1.500E-010.000E+001.500E-013.000E-014.500E-016.000E-017.500E-019.000E-019.964E-01

-5.0

37E

-04

1.78

4E-0

2 8

.076

E-03

8.516E-03

-2.745E-02

-1.00

6E-03 -8

.330

E-03 5.324E-03

-2.763E-02

1.752E-02

-5.0

99E

-04

1.2

52E

-04

-1.248E-01

-4.2

36E-

02

-4.766E-02

-4.427E-02

-6.749E-02 -6.697E-02

-1.258E-01 1.0

81E

-04

Tunnels

of

New Railway Connection in Prague Analysis

of plain

concrete

tunnel

lining


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Shopping

Mall

in Prague heavy reinforced girder with large openings


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Shopping

Mall

in Prague heavy reinforced girder with large openings

LOAD-DISPLACEMENT RESPONSE

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

deflection [mm]

load

inte

nsity

[kN

/m2]

full

circular opening strong

circular opening, ties

circular opening

service load 12 kN/m2

dead load 7.75 kN/m2


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Prestressed

concrete containment in nuclear power plant

SAFETY


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Features of virtual testing of structures (nonlinear computer simulation):

detailed information about structural response

and behavior under various actions

ultimate load-carrying capacity,

resistance

against expected load, overloading

mechanical damage

in reinforced concrete structures (cracking, crushing)

serviceability

simulating failureexplanation of reasons

predictionprevention

avoidance


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VIRTUAL TESTING

Nonlinear computer simulation of damage in concrete structures

Probabilistic-based assessment of structural safety and reliability

uncertainty, randomness, stochastic evaluation


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SARA main

components:


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Stochastic methods

Improved results:

statistical characteristics of structural responsesensitivity analysisassessment of

structural

safety, reliability, failure

probabilitystatistical size-effect

Improved input parameters

for nonlinear analysis:

reflects real material and structural properties uncertain (lack of information)set

of

random

data measured in material tests


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Repeated nonlinear analysis

standard stochastic method: Monte Carlo high number of realizations

required

demanding nonlinear FE analysis

-

contradiction

probabilistic methods suitable for nonlinear analysis

stratified Monte Carlo -

Latin Hypercube Sampling

(LHS)small number of realizations

for acceptable accurate results

methodology:random sets of input parameters are generated

and used in nonlinear analysis


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Latin Hypercube Sampling (LHS)

statistical correlation

between random variables –

undesired, desired –

correlation matrix

random variables

real

izat

ions

permutation of samples


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probabilitydensity

load,

resistanceR=2.5 MN,COV 0.102

Load E

assumption: normal distribution

ERZ μμμ −=222ERZ σσσ +=

Z

Zσμβ =

Reliability assessment -

Cornell’s β-index


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012345678

0.5 1 1.5 2 2.5

Load [MN]

Rel

iabi

lity

inde

x COV of load = 0.1COV of load = 0.2Eurocode

Reliability index β


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Software FReET

Feasible Reliability Engineering Tooldeveloped by Reliability group at TU Brno (Prof. Drahomír

Novák)designed for

computationally intensive applications

main functions:

randomization of input databuilt-in database of statistic parameters of concrete and reinforcement propertiessimulated annealing method for imposing statistical correlation

(weighted, non-positive definite correlation matrix)

stochastic evaluation

of results (structural resistance, crack width)histogram, mean, COV, distribution type

(suitability

check), limit state function

sensitivity

analysis (importance of input parameters)based on nonparametric rank-order statistical correlation

reliability and safety assessmentusing reliability index and theoretical failure probability


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Software FReET

reliability techniques:

Cornell’s reliability β-indexFORMSORMdesign pointHasofer-Lind reliability indexresponse surface methodology in failure region – polynomial approximation (Bucher-Bourgund approach) importance sampling (around mean values or around design point)


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SARA system

Virtual testing of bridges for life cycle reliability assessment

open architecture:identification of optimal input parametersdamage identification

life-cycle

reliability assessment:

degradation and deterioration analysisprediction of structural reliability evolutionlife-cycle analysis, retrofitting and rehabilitation, cost optimization


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SARA main

components:


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Degradation of structures –

FReET–D

developed at TU Brno by group of Prof. Břetislav Teplý

phenomenological models for material degradation

Carbonation of Concrete (depasivation):

• Papadakis

1992

• Papadakis

2002

• Morinaga 1988

• Morinaga 2002

• Linhua+Jiang

–

OPC

• Linhua+Jiang

–

HVFA

• Bob+Affana

• Kishitany

• fib Model Code

Chloride Ingress:

• Papadakis

1992

• fib Model Code

Reinforcement Corrosion:

• Andrade

Stress

Corrosion Cracking – prestressed

steel


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Papadakis

1992

( ) tccρaρ

cwρ

RHf

cwρ

.cw

ρ.x COa

cc

ccc

61044

8.231000

1

10001

30350

2

−⎟⎟⎠

⎞⎜⎜⎝

⎛++

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎟⎠⎞

⎜⎝⎛ −

=

Papadakis

2002

)(218.0

1044

8.232 6, 22

kPc

tcDx

COCOe

c +=

−

Morinaga

1988

Morinaga

2002

for w/c ≤

0.6:

for w/c > 0.6:

21

61044

8.23)(38.016502

⎟⎠⎞

⎜⎝⎛ ⋅⋅⎟

⎠⎞

⎜⎝⎛ −≈ − tcRHfcwx COc

( )( )[ ]

21

6

21

1044

8.23)(6.21

25.01650

2⎟⎠⎞

⎜⎝⎛ ⋅⋅

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+

−≈ − tcRHf

cw

cwx COc

for w/c ≥

0.6:

for w/c ≤

0.6:

tWTRHRCOxc )76.16.4)(0217.0174.0391.1(44.25/2 −+−⋅⋅=

( )( ) tWWTRHRCOxc 315.1/)25.09.4)0217.0174.0391.1(44.25/2 +−+−⋅⋅=

Carbonation of Concrete


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Linhua+Jiang

-

OPC

Bob+Affana

Kishitany

Linhua+Jiang

-

HVFA

( ) tccrr

crw

RHx COcHD

cc ⋅⋅

−⋅−= −41.1 10

448.23

34.01839

2

( ) nCOc tc

ckBWRHx ⋅⋅

−⋅−⋅= −4

'

*1.1 10

448.2334.0/1839

2α

tfdkCx

cc 150=

for w/c < 0.6:

for w/c > 0.6:

( )[ ] tcwRxc ⋅−⋅

=2.7

76.1/6.410

( )[ ]( )[ ]

tcw

cwRxc ⋅+−⋅

=/315.13.025.0/10

fib

Model Code

( ) WTcRkkkTx COtOACCtcec ⋅⋅⋅+⋅⋅⋅⋅= −− 61, 102)(

2ε

Input parameters –

random and/or uncertain


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Linhua+Jiang

-

OPC

Bob+Affana

Kishitany

Linhua+Jiang

-

HVFA

( ) tccrr

crw

RHx COcHD

cc ⋅⋅

−⋅−= −41.1 10

448.23

34.01839

2

( ) nCOc tc

ckBWRHx ⋅⋅

−⋅−⋅= −4

'

*1.1 10

448.2334.0/1839

2α

tfdkCx

cc 150=

for w/c < 0.6:

for w/c > 0.6:

( )[ ] tcwRxc ⋅−⋅

=2.7

76.1/6.410

( )[ ]( )[ ]

tcw

cwRxc ⋅+−⋅

=/315.13.025.0/10

fib

Model Code

( ) WTcRkkkTx COtOACCtcec ⋅⋅⋅+⋅⋅⋅⋅= −− 61, 102)(

2ε

Parametric function library in FReET


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Andrade

( ) ( )( )⎪

⎩

⎪⎨

⎧

+>+≤<−−

≤=

ααα

corrii

corriiiicorri

ii

idTtidTtTTtid

Ttdtd

116.0/0116.0/116.0)(

Results

of the degradation analysis

–

probability distribution function

used for the stochastic nonlinear FE analysis

Chaining of the models:

1. Depassivation

time

2. Steel Corrosion


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Summary

and

Conclusions

Combination of efficient methods:

• virtual testing (nonlinear FE analysis)

• reliability assessment (stochastic evaluation)

• degradation models

(life cycle analysis)

Evaluation

of existing

structures (reliability, probability of failure) –

relative

comparison

Life-cycle

analysis

–

degradation

+ retrofitting

Traces

evolution

of structural

reliability

in time

Design for durability

(Performance Based

Design)

Mean service life

Sevice life density

TimeFailure probability

Target service life

Distribution ofS(t)

S(t)

R(t)

R,SPf

Pf

Distribution of R(t)


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Precast prestressed

bridge girder AASHTO Type IV

damaged by hydrogen induced SCC (Stress Corrosion Cracking)

Illustrative example:


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• 26 prestressing

strands

• 2D plane stress with variable thickness

• about 3000 elements and 4500 nodes

• continuous loading (cov

= 0.0 and 0.2)

•

nonlinear solution using Newton-

Rhapson

algorithm

Illustrative example:


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Material properties


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Correlation matrix

upper right triangle = prescribed, lower left triangle = generated for 40 realizations)


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Deterministic and stochastic analysis

Several alternatives calculated:

• virgin state

• 2 strands ruptured

• 6 strands ruptured

• bond renewed

Typical

crack

pattern

at

ultimate

load


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Load-deflection

diagrams


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Failure

probability


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Reliability

index


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Thank you for your attention

www.cervenka.cz

[email protected]

virtual testing of bridges for life cycle reliability...

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